# Ford Circles with Variable Radii

Ford Circles with Variable Radii

Ford circles are centered at ,, with radii , where and are coprime integers. Each circle is tangent to the axis at and to two circles from earlier iterations. This Demonstration shows the Ford circles with the extra feature that the radii of the two largest circles are variable. Thus, in each direction, the scaling of the circle of the next level is different. Iteration generates +1 circles. In the limit , each circle becomes tangent to infinitely many other circles.

h

k

1

2

2

k

1

2

2

k

h

k

x

h

k

n

n

2

n→∞